Stochastic Development Regression on Non-Linear Manifolds

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes

XMM-Newton view of Swift J1834.9-0846 and its Magnetar Wind Nebula

We report on the analysis of two XMM-Newton observations of the recently discovered soft gamma repeater Swift J1834.9-0846, taken in September 2005 and one month after the source went into outburst on 2011 August 7. We performed timing and spectral analyses on the point source as well as on the extended emission. We find that the source period is consistent with an extrapolation of the Chandra ephemeris reported earlier and the spectral properties remained constant. The source luminosity decreased to a level of 1.6x10^34 erg s^-1 following a decay trend of $\propto t^{-0.5}$. Our spatial analysis of the source environment revealed the presence of two extended emission regions around the source. The first (Region A) is a symmetric ring around the point source, starting at 25arcsec and extending to ~50arcsec. We argue that Region A is a dust scattering halo. The second (Region B) has an asymmetrical shape extending between 50arcsec and 150arcsec, and is detected both in the pre- and post-outburst data. We argue that this region is a possible magnetar wind nebula (MWN). The X-ray efficiency of the MWN with respect to the rotation energy loss is substantially higher than those of rotation powered pulsars: $\eta_{\rm X}\equiv L_{\rm MWN,0.5-8 keV}/\dot{E}_{\rm rot}\approx0.7$. The higher efficiency points to a different energy source for the MWN of Swift J1834.9-0846, most likely bursting activity of the magnetar, powered by its high magnetic field, B=1.4x10^14 G.Comment: 10 pages, 10 figures, accepted for publication in Ap

On the Complexity of Temporal-Logic Path Checking

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC. In this paper, we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of writing, MTL is the most expressive logic with an NC path-checking algorithm, and UTL is the most expressive fragment of LTL with a more efficient path-checking algorithm than for full LTL (subject to standard complexity-theoretic assumptions). We then establish a connection between LTL path checking and planar circuits, which we exploit to show that any further progress in determining the precise complexity of LTL path checking would immediately entail more efficient evaluation algorithms than are known for a certain class of planar circuits. The connection further implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem